naa a22 4500 510811566 CHVBK 20180411083444.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1134/S0081543813010100 doi (NATIONALLICENCE)springer-10.1134/S0081543813010100 Some classes of functions and Fourier coefficients with respect to general orthonormal systems [Elektronische Daten] [L. Gogoladze, V. Tsagareishvili] The a.e. convergence of an orthogonal series on [0, 1] depends strongly on the coefficients of this series. It is well known that a sufficient condition for the a.e. convergence of such a series is given by the Men'shov-Rademacher theorem. On the other hand, S. Banach proved that good differential properties of a function do not guarantee the a.e. convergence on [0, 1] of the Fourier series of this function with respect to general orthonormal systems (ONSs). In the present study, we find conditions on the functions of an ONS under which the Fourier coefficients of functions of some differential classes satisfy the hypothesis of the Men'shov-Rademacher theorem. Pleiades Publishing, Ltd., 2013 Gogoladze L. I. Javakhishvili Tbilisi State University, Chavchavadze Ave. 1, 0218, Tbilisi, Georgia aut Tsagareishvili V. I. Javakhishvili Tbilisi State University, Chavchavadze Ave. 1, 0218, Tbilisi, Georgia aut Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280/1(2013-04-01), 156-168 0081-5438 280:1<156 2013 280 11501 https://doi.org/10.1134/S0081543813010100 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813010100 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gogoladze L. I. Javakhishvili Tbilisi State University, Chavchavadze Ave. 1, 0218, Tbilisi, Georgia aut NATIONALLICENCE 700 1- Tsagareishvili V. I. Javakhishvili Tbilisi State University, Chavchavadze Ave. 1, 0218, Tbilisi, Georgia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280/1(2013-04-01), 156-168 0081-5438 280:1<156 2013 280 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer